67 research outputs found
A containment result in and the Chudnovsky conjecture
In the paper we prove the containment , for a
radical ideal of general points in , where .
As a corollary we get that the Chudnovsky Conjecture holds for a very general
set of at least points in .Comment: 5 pages. To appear in PAM
A vanishing theorem and symbolic powers of planar point ideals
The purpose of this note is twofold. We present first a vanishing theorem for
families of linear series with base ideal being a fat points ideal. We apply
then this result in order to give a partial proof of a conjecture raised by
Bocci, Harbourne and Huneke concerning containment relations between ordinary
and symbolic powers of planar point ideals.Comment: 17 page
Asymptotic Hilbert Polynomial and limiting shapes
The main aim of this paper is to provide a method which allows finding
limiting shapes of symbolic generic initial systems of higher-dimensional
subvarieties of P^n. M. Mustata and S. Mayes established a connection between
volumes of complements of limiting shapes and the asymptotic multiplicity for
ideals of points. In the paper we prove a generalization of this fact to
higher-dimensional sets
Symbolic powers of planar point configurations
We study initial degrees of symbolic powers of ideals of arbitrary finite
sets of points in the projective plane over an algebraically closed field of
characteristic zero. We show, how bounds on the growth of these degrees
determine the geometry of the given set of points.Comment: 18 page
Symbolic powers of planar point configurations II
We study initial sequences of various configurations of planar points. We
answer several questions asked in our previous paper (Symbolic powers of planar
point configurations), and we extend our considerations to the asymptotic
setting of Waldschmidt constants. We introduce the concept of Bezout
Decomposition which might be of independent interest.Comment: This article is a sequel to arXiv:1205.6002. 15 page
Symbolic generic initial systems of star configurations
The purpose of this note is to describe limiting shapes (as introduced by
Mayes) of symbolic generic initial systems of star configurations in projective
spaces over a field of characteristic 0.Comment: 8 page
Points fattening on P^1 x P^1 and symbolic powers of bi-homogeneous ideals
We study symbolic powers of bi-homogeneous ideals of points in the Cartesian
product of two projective lines and extend to this setting results on the
effect of points fattening obtained by Bocci, Chiantini and Dumnicki, Szemberg,
Tutaj-Gasi\'nska. We prove a Chudnovsky-type theorem for bi-homogeneous ideals
and apply it to classification of configurations of points with minimal or no
fattening effect. We hope that the ideas developed in this project will find
further algebraic and geometric applications e.g. to study similar problems on
arbitrary surfaces.Comment: 12 pages, notes from a workshop on linear series held in Lanckoron
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